Question

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How to split text without spaces into list of words?

There are masses of text information in people’s comments which are parsed from html, but there are no delimiting characters in them. For example: thumbgreenappleactiveassignmentweeklymetaphor. Apparently, there are ‘thumb’, ‘green’, ‘apple’, etc. in the string. I also have a large dictionary to query whether the word is reasonable.
So, what’s the fastest way to extract these words?

Answer 1

I’m not really sure a naive algorithm would serve your purpose well, as pointed out by eumiro, so I’ll describe a slightly more complex one.

The idea

The best way to proceed is to model the distribution of the output. A good first approximation is to assume all words are independently distributed. Then you only need to know the relative frequency of all words. It is reasonable to assume that they follow Zipf’s law, that is the word with rank n in the list of words has probability roughly 1/(n log N) where N is the number of words in the dictionary.

Once you have fixed the model, you can use dynamic programming to infer the position of the spaces. The most likely sentence is the one that maximizes the product of the probability of each individual word, and it’s easy to compute it with dynamic programming. Instead of directly using the probability we use a cost defined as the logarithm of the inverse of the probability to avoid overflows.

The code

import math

# Build a cost dictionary, assuming Zipf's law and cost = -math.log(probability).
words = open("words-by-frequency.txt").read().split()
wordcost = dict((k,math.log((i+1)*math.log(len(words)))) for i,k in enumerate(words))
maxword = max(len(x) for x in words)

def infer_spaces(s):
    """Uses dynamic programming to infer the location of spaces in a string
    without spaces."""

    # Find the best match for the i first characters, assuming cost has
    # been built for the i-1 first characters.
    # Returns a pair (match_cost, match_length).
    def best_match(i):
        candidates = enumerate(reversed(cost[max(0, i-maxword):i]))
        return min((c + wordcost.get(s[i-k-1:i], 9e999), k+1) for k,c in candidates)

    # Build the cost array.
    cost = [0]
    for i in range(1,len(s)+1):
        c,k = best_match(i)
        cost.append(c)

    # Backtrack to recover the minimal-cost string.
    out = []
    i = len(s)
    while i>0:
        c,k = best_match(i)
        assert c == cost[i]
        out.append(s[i-k:i])
        i -= k

    return " ".join(reversed(out))

which you can use with

s = 'thumbgreenappleactiveassignmentweeklymetaphor'
print(infer_spaces(s))

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Examples

I am using this quick-and-dirty 125k-word dictionary I put together from a small subset of Wikipedia.

Before: thumbgreenappleactiveassignmentweeklymetaphor.
After: thumb green apple active assignment weekly metaphor.

Before: thereismassesoftextinformationofpeoplescommentswhichisparsedfromhtmlbuttherearen
odelimitedcharactersinthemforexamplethumbgreenappleactiveassignmentweeklymetapho
rapparentlytherearethumbgreenappleetcinthestringialsohavealargedictionarytoquery
whetherthewordisreasonablesowhatsthefastestwayofextractionthxalot.

After: there is masses of text information of peoples comments which is parsed from html but there are no delimited characters in them for example thumb green apple active assignment weekly metaphor apparently there are thumb green apple etc in the string i also have a large dictionary to query whether the word is reasonable so what s the fastest way of extraction thx a lot.

Before: itwasadarkandstormynighttherainfellintorrentsexceptatoccasionalintervalswhenitwascheckedbyaviolentgustofwindwhichsweptupthestreetsforitisinlondonthatoursceneliesrattlingalongthehousetopsandfiercelyagitatingthescantyflameofthelampsthatstruggledagainstthedarkness.

After: it was a dark and stormy night the rain fell in torrents except at occasional intervals when it was checked by a violent gust of wind which swept up the streets for it is in london that our scene lies rattling along the housetops and fiercely agitating the scanty flame of the lamps that struggled against the darkness.

As you can see it is essentially flawless. The most important part is to make sure your word list was trained to a corpus similar to what you will actually encounter, otherwise the results will be very bad.

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Optimization

The implementation consumes a linear amount of time and memory, so it is reasonably efficient. If you need further speedups, you can build a suffix tree from the word list to reduce the size of the set of candidates.

If you need to process a very large consecutive string it would be reasonable to split the string to avoid excessive memory usage. For example you could process the text in blocks of 10000 characters plus a margin of 1000 characters on either side to avoid boundary effects. This will keep memory usage to a minimum and will have almost certainly no effect on the quality.